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Simplifying x2 + -34x + -12 = 0 Reorder the terms: -12 + -34x + x2 = 0 Solving -12 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -34x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -34x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -34x + x2 = 0 + 12 -34x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -34x + x2 = 12 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 12 + 289 Reorder the terms: 289 + -34x + x2 = 12 + 289 Combine like terms: 12 + 289 = 301 289 + -34x + x2 = 301 Factor a perfect square on the left side: (x + -17)(x + -17) = 301 Calculate the square root of the right side: 17.349351573 Break this problem into two subproblems by setting (x + -17) equal to 17.349351573 and -17.349351573.Subproblem 1
x + -17 = 17.349351573 Simplifying x + -17 = 17.349351573 Reorder the terms: -17 + x = 17.349351573 Solving -17 + x = 17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 17.349351573 + 17 Combine like terms: -17 + 17 = 0 0 + x = 17.349351573 + 17 x = 17.349351573 + 17 Combine like terms: 17.349351573 + 17 = 34.349351573 x = 34.349351573 Simplifying x = 34.349351573Subproblem 2
x + -17 = -17.349351573 Simplifying x + -17 = -17.349351573 Reorder the terms: -17 + x = -17.349351573 Solving -17 + x = -17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -17.349351573 + 17 Combine like terms: -17 + 17 = 0 0 + x = -17.349351573 + 17 x = -17.349351573 + 17 Combine like terms: -17.349351573 + 17 = -0.349351573 x = -0.349351573 Simplifying x = -0.349351573Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.349351573, -0.349351573}
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